The fallacy is in imagining it is meaningful to separate money (earned or otherwise) from the system of government it was generated in. Your ability to "earn the money" is fundamentally tied to this system, and if you change one, you change the other necessarily (not a comment on the direction of the delta). Thinking about the economy as a thing that exists on its own, and the government as an institution that just "takes away" from this is just nonsensical.
The statement "It's not as if with government we have more money" is quite likely a category error. After all the ideas of money and the ideas of government are so deeply intertwined in their evolution that people haven't managed to separate them, ahistorical thought experiments in common introductory economics notwithstanding.
For what it's worth, I am sympathetic to some of the arguments you are heading towards, I just object to the sloppy thinking variants of them - which are the most common, unfortunately.
You don't even have to look at history, you can look around the world today with failed states and black markets. Wherever there are people there is economic activity ("earn money"). If there is no state, groups and individuals take upon themselves those roles which the state has monopoly in most places: protection of private property and dispute resolution. These two things are the most vital ingredients for economic activity.
> After all the ideas of money and the ideas of government are so deeply intertwined in their evolution that people haven't managed to separate them
You're just making an unfounded assertion. Many people separate economy and state, for good reason. Money have existed and exist today (cryptocurrencies for one example) irrespective of government.
[edit: I had a longer response but realize it opened up a bunch of side issues that weren't helpful]
The economy and the system of government it operates in (yes, including black/grey markets) are fundamentally intertwined in ways that make it hard to reason about separately.
What I'm objecting to are statements that boil down to: "If we all paid X less tax I would have X more dollars which we could do as we please with". In general this is hopelessly naive.
For what it is worth, both your examples of failed states and cryptocurrrencies (which do not, yet?, operate as currencies) support exactly what I am talking about, not the converse.
The attempt to divide an conquer in thinking about economies and government is useful but so far not completely successful. When it leads to people making silly inferences, it is problematic. So yes people talk about them as if they were separate, because it is easier. But that is not the same as having separated them.
Furthermore, the idea that private charity is inherently more efficient than government is far from self-evident. A basic income policy, for example, could be a far more comprehensive and efficient way of directly addressing poverty than a patchwork of charities targeted specific symptoms of poverty. This is one reason that many pragmatic libertarians are actually favorable toward basic income.
Many states have tax deductions on charitable donations. They're mostly used by wealthy people to shirk their taxes by "donating" to a "charity" that serves their own interests (e.g. "donating" a valuable painting to an "art museum" they establish next door to their house, open only by appointment with them).
It's not as if with government we have more money. So all that matters is efficiency and if a charity is more efficient than a government, why is there no state where you can choose whom to give (at least part of) your taxes?